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2007, Volume 17, Issue 3: 481-500. Doi: 10.3934/dcds.2007.17.481
This issue Previous Article On the Euler-Lagrange equation for a variational problem Next Article On the number of ergodic minimizing measures for Lagrangian flows

On the convergence of solutions of the Leray-$\alpha $ model to the trajectory attractor of the 3D Navier-Stokes system

  • 1.

    Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 127994, GSP-4

  • 2.

    Department of Mathematics and Department of Mechanics and Aerospace Engineering, University of California, Irvine, CA 92697

Received:  December 31, 2005
Revised:  July 31, 2006
Published:  August 2007
Abstract Related Papers Cited by
    Abstract
  • We study the relations between the global dynamics of the 3D Leray-$\alpha $ model and the 3D Navier-Stokes system. We prove that time shifts of bounded sets of solutions of the Leray-$\alpha $ model converges to the trajectory attractor of the 3D Navier-Stokes system as time tends to infinity and $ \alpha $ approaches zero. In particular, we show that the trajectory attractor of the Leray-$\alpha $ model converges to the trajectory attractor of the 3D Navier-Stokes system when $\alpha \rightarrow 0\+.$
    Mathematics Subject Classification: Primary: 35Q30, 37L30; Secondary: 76D03, 76F20, 76F55, 76F65.

    Citation:
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